ML MRB2 - Revision history

Karsai at 11:56, 31 March 2023

2023-03-31T11:56:16Z

← Older revision		Revision as of 11:56, 31 March 2023
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	{{DISPLAYTITLE:ML_MRB2}}		{{DISPLAYTITLE:ML_MRB2}}
	{{TAGDEF\|ML_MRB2\|[integer]\|~~{{TAG\|ML_MRB1}}~~}}		{{TAGDEF\|ML_MRB2\|[integer]\|8}}

	Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand the angular descriptor within the machine learning force field method.		Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand the angular descriptor within the machine learning force field method.

Karsai: /* Related tags and articles */

2022-04-08T13:29:04Z

Karsai at 07:36, 7 April 2022

2022-04-07T07:36:05Z

← Older revision		Revision as of 07:36, 7 April 2022
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			{{DISPLAYTITLE:ML_MRB2}}
	{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}}}		{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}}}

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	{{NB\|mind\|The number of angular descriptor expansion coefficients <math>p_{n\nu l}^{i}</math> scales '''quadratically''' with <math>N_\text{R}^l</math> set by this tag. It also depends on {{TAG\|ML_LMAX2}} and the number of elements.}}		{{NB\|mind\|The number of angular descriptor expansion coefficients <math>p_{n\nu l}^{i}</math> scales '''quadratically''' with <math>N_\text{R}^l</math> set by this tag. It also depends on {{TAG\|ML_LMAX2}} and the number of elements.}}

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_LMAX2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_SION2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_LMAX2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_SION2}}

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	----		----

	[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields~~]][[Category: Alpha~~]]		[[Category:INCAR tag]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]]

Singraber at 13:54, 13 October 2021

2021-10-13T13:54:51Z

← Older revision		Revision as of 13:54, 13 October 2021
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	</math>		</math>

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers <math>p_{n\nu l}^{i}</math> by expanding it into a set of radial basis functions <math>\chi_{nl}(r)</math> and Legendre polynomials <math>P_{l}</math> (see [[Machine learning force field: Theory#Basis set expansion\|this section]] for more details):		and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers <math>p_{n\nu l}^{i}</math> by expanding it into a set of radial basis functions <math>\chi_{nl}(r)</math> and Legendre polynomials <math>P_{l}\left(\mathrm{cos}\theta\right)</math> (see [[Machine learning force field: Theory#Basis set expansion\|this section]] for more details):

	<math>		<math>
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	The tag {{TAG\|ML_MRB2}} sets the number <math>N_\text{R}^l</math> of radial basis functions to use in this expansion. The same number is used for all <math>l</math>.		The tag {{TAG\|ML_MRB2}} sets the number <math>N_\text{R}^l</math> of radial basis functions to use in this expansion. The same number is used for all <math>l</math>.
			{{NB\|mind\|The number of angular descriptor expansion coefficients <math>p_{n\nu l}^{i}</math> scales '''quadratically''' with <math>N_\text{R}^l</math> set by this tag. It also depends on {{TAG\|ML_LMAX2}} and the number of elements.}}

	== Related Tags and Sections ==		== Related Tags and Sections ==

Singraber at 12:44, 13 October 2021

2021-10-13T12:44:20Z

← Older revision		Revision as of 12:44, 13 October 2021
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	{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}}}		{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}}}

	Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand ~~the atomic distribution for~~ the angular descriptor within the machine learning force field method ~~as described in [[Machine learning force field: Theory#Descriptors\|this section]]~~.		Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand the angular descriptor within the machine learning force field method.
	----		----
			The angular descriptor is constructed from

			<math>
			\rho_{i}^{(3)}\left(r,s,\theta\right) = \iint d\hat{\mathbf{r}} d\hat{\mathbf{s}} \delta\left(\hat{\mathbf{r}}\cdot\hat{\mathbf{s}} - \mathrm{cos}\theta\right) \sum\limits_{j=1}^{N_{a}} \sum\limits_{k \ne j}^{N_{a}} \rho_{ik} \left(r\hat{\mathbf{r}}\right) \rho_{ij} \left(s\hat{\mathbf{s}}\right), \quad \text{where} \quad
			\rho_{ij}\left(\mathbf{r}\right) = f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right)
			</math>

			and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers <math>p_{n\nu l}^{i}</math> by expanding it into a set of radial basis functions <math>\chi_{nl}(r)</math> and Legendre polynomials <math>P_{l}</math> (see [[Machine learning force field: Theory#Basis set expansion\|this section]] for more details):

			<math>
			\rho_{i}^{(3)}\left(r,s,\theta\right) = \sum\limits_{l=1}^{L_{\mathrm{max}}} \sum\limits_{n=1}^{N^{l}_{\mathrm{R}}}\sum\limits_{\nu=1}^{N^{l}_{\mathrm{R}}} \sqrt{\frac{2l+1}{2}} p_{n\nu l}^{i}\chi_{nl}\left(r\right)\chi_{\nu l}\left(s\right)P_{l}\left(\mathrm{cos}\theta\right).
			</math>

			The tag {{TAG\|ML_MRB2}} sets the number <math>N_\text{R}^l</math> of radial basis functions to use in this expansion. The same number is used for all <math>l</math>.

	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_SION2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_LMAX2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_SION2}}

	{{sc\|ML_MRB2\|Examples\|Examples that use this tag}}		{{sc\|ML_MRB2\|Examples\|Examples that use this tag}}

Singraber at 16:12, 11 October 2021

2021-10-11T16:12:27Z

← Older revision		Revision as of 16:12, 11 October 2021
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	Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand the atomic distribution for the angular descriptor within the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors\|this section]].		Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand the atomic distribution for the angular descriptor within the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors\|this section]].
	----		----


	== Related Tags and Sections ==		== Related Tags and Sections ==

Singraber at 16:12, 11 October 2021

2021-10-11T16:12:03Z

← Older revision		Revision as of 16:12, 11 October 2021
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	{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}~~/1.5~~}}		{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}}}

	Description: This tag sets the number of radial basis ~~sets~~ used to expand the atomic distribution for the angular descriptor within the machine learning force field method.		Description: This tag sets the number <math>N_\text{R}^l</math> (for all <math>l</math>) of radial basis functions used to expand the atomic distribution for the angular descriptor within the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors\|this section]].
	----		----
	The values for {{TAG\|ML_MRB1}} and {{TAG\|ML_MRB2}} are automatically set by the code (empirically) and usually need not to be set by the user. Only in very few cases if the error in the radial expansion (see later in the text) is not sufficiently low these values need to be adjusted manually.

	The tags {{TAG\|ML_MRB1}} and {{TAG\|ML_MRB2}} set the number of radial basis sets used to expand the atomic distribution of the radial and angular density. These tags depend very sensitively on the cut-off radius of the descriptor ({{TAG\|ML_RCUT1}} and {{TAG\|ML_RCUT2}}) and the width of the Gaussian functions used in the broadening of the atomic distributions ({{TAG\|ML_SION1}} and {{TAG\|ML_SION2}}). The error occuring due to the expansion of the radial basis functions is monitored in the {{TAG\|ML_LOGFILE}} file by searching for the following line "''Error in radial expansion: ...''". A typical reasonable value for the error threshold that was empirically determined (by us and in reference {{cite\|szlachta:prb:2014}}) is <math>\pm 0.02</math>. Hence, the number of basis functions should be adjusted until the error written in the {{TAG\|ML_LOGFILE}} is smaller than this value. A more detailed description of the basis sets is given in appendix A of reference {{cite\|jinnouchi2:arx:2019}}.



	~~== References ==~~
	~~<references/>~~

	~~<noinclude>~~
	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1~~}}, {{TAG\|ML_RCUT1~~}}, {{TAG\|ML_RCUT2~~}}, {{TAG\|ML_SION1~~}}, {{TAG\|ML_SION2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_SION2}}

	{{sc\|ML_MRB2\|Examples\|Examples that use this tag}}		{{sc\|ML_MRB2\|Examples\|Examples that use this tag}}

Karsai at 09:05, 23 August 2021

2021-08-23T09:05:57Z

← Older revision		Revision as of 09:05, 23 August 2021
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	{{TAGDEF\|~~ML_FF_MRB2_MB~~\|[integer]\|{{TAG\|~~ML_FF_MRB1_MB~~}}/1.5}}		{{TAGDEF\|ML_MRB2\|[integer]\|{{TAG\|ML_MRB1}}/1.5}}

	Description: This tag sets the number of radial basis sets used to expand the atomic distribution for the angular descriptor within the machine learning force field method.		Description: This tag sets the number of radial basis sets used to expand the atomic distribution for the angular descriptor within the machine learning force field method.
	----		----
	The values for {{TAG\|~~ML_FF_MRB1_MB~~}} and {{TAG\|~~ML_FF_MRB2_MB~~}} are automatically set by the code (empirically) and usually need not to be set by the user. Only in very few cases if the error in the radial expansion (see later in the text) is not sufficiently low these values need to be adjusted manually.		The values for {{TAG\|ML_MRB1}} and {{TAG\|ML_MRB2}} are automatically set by the code (empirically) and usually need not to be set by the user. Only in very few cases if the error in the radial expansion (see later in the text) is not sufficiently low these values need to be adjusted manually.

	The tags {{TAG\|~~ML_FF_MRB1_MB~~}} and {{TAG\|~~ML_FF_MRB2_MB~~}} set the number of radial basis sets used to expand the atomic distribution of the radial and angular density. These tags depend very sensitively on the cut-off radius of the descriptor ({{TAG\|~~ML_FF_RCUT1_MB~~}} and {{TAG\|~~ML_FF_RCUT2_MB~~}}) and the width of the Gaussian functions used in the broadening of the atomic distributions ({{TAG\|~~ML_FF_SION1_MB~~}} and {{TAG\|~~ML_FF_SION2_MB~~}}). The error occuring due to the expansion of the radial basis functions is monitored in the {{TAG\|ML_LOGFILE}} file by searching for the following line "''Error in radial expansion: ...''". A typical reasonable value for the error threshold that was empirically determined (by us and in reference {{cite\|szlachta:prb:2014}}) is <math>\pm 0.02</math>. Hence, the number of basis functions should be adjusted until the error written in the {{TAG\|ML_LOGFILE}} is smaller than this value. A more detailed description of the basis sets is given in appendix A of reference {{cite\|jinnouchi2:arx:2019}}.		The tags {{TAG\|ML_MRB1}} and {{TAG\|ML_MRB2}} set the number of radial basis sets used to expand the atomic distribution of the radial and angular density. These tags depend very sensitively on the cut-off radius of the descriptor ({{TAG\|ML_RCUT1}} and {{TAG\|ML_RCUT2}}) and the width of the Gaussian functions used in the broadening of the atomic distributions ({{TAG\|ML_SION1}} and {{TAG\|ML_SION2}}). The error occuring due to the expansion of the radial basis functions is monitored in the {{TAG\|ML_LOGFILE}} file by searching for the following line "''Error in radial expansion: ...''". A typical reasonable value for the error threshold that was empirically determined (by us and in reference {{cite\|szlachta:prb:2014}}) is <math>\pm 0.02</math>. Hence, the number of basis functions should be adjusted until the error written in the {{TAG\|ML_LOGFILE}} is smaller than this value. A more detailed description of the basis sets is given in appendix A of reference {{cite\|jinnouchi2:arx:2019}}.


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	<noinclude>		<noinclude>
	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|~~ML_FF_LMLFF~~}}, {{TAG\|~~ML_FF_MRB1_MB~~}}, {{TAG\|~~ML_FF_W1_MB~~}}, {{TAG\|~~ML_FF_W1_MB~~}}, {{TAG\|~~ML_FF_RCUT1_MB~~}}, {{TAG\|~~ML_FF_RCUT2_MB~~}}, {{TAG\|~~ML_FF_SION1_MB}}, {{TAG\|ML_FF_SION2_MB~~}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_W1}}, {{TAG\|ML_RCUT1}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}

	{{sc\|~~ML_FF_MRB2_MB~~\|Examples\|Examples that use this tag}}		{{sc\|ML_MRB2\|Examples\|Examples that use this tag}}
	----		----

	[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]		[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]][[Category: Alpha]]

Karsai: Karsai moved page ML FF MRB2 MB to ML MRB2

2021-08-23T06:46:51Z

Karsai moved page ML FF MRB2 MB to ML MRB2

← Older revision	Revision as of 06:46, 23 August 2021
(No difference)

Karsai at 07:40, 8 June 2021

2021-06-08T07:40:40Z

← Older revision		Revision as of 07:40, 8 June 2021
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	{{TAGDEF\|ML_FF_MRB2_MB\|[integer]\|{{TAG\|ML_FF_MRB1_MB}}/1.5}}		{{TAGDEF\|ML_FF_MRB2_MB\|[integer]\|{{TAG\|ML_FF_MRB1_MB}}/1.5}}

	Description: This tag sets the number of radial basis sets used to expand the atomic distribution for the angular descriptor within the machine learning force field method~~. The code automatically determine {{TAG\|ML_FF_MRB2_MB}} in such a way~~		Description: This tag sets the number of radial basis sets used to expand the atomic distribution for the angular descriptor within the machine learning force field method.
	~~the the error "Error in radial expansion:" in the {{TAG\|ML_LOGFILE}} is below a threshold~~.
	----		----
			The values for {{TAG\|ML_FF_MRB1_MB}} and {{TAG\|ML_FF_MRB2_MB}} are automatically set by the code (empirically) and usually need not to be set by the user. Only in very few cases if the error in the radial expansion (see later in the text) is not sufficiently low these values need to be adjusted manually.

			The tags {{TAG\|ML_FF_MRB1_MB}} and {{TAG\|ML_FF_MRB2_MB}} set the number of radial basis sets used to expand the atomic distribution of the radial and angular density. These tags depend very sensitively on the cut-off radius of the descriptor ({{TAG\|ML_FF_RCUT1_MB}} and {{TAG\|ML_FF_RCUT2_MB}}) and the width of the Gaussian functions used in the broadening of the atomic distributions ({{TAG\|ML_FF_SION1_MB}} and {{TAG\|ML_FF_SION2_MB}}). The error occuring due to the expansion of the radial basis functions is monitored in the {{TAG\|ML_LOGFILE}} file by searching for the following line "''Error in radial expansion: ...''". A typical reasonable value for the error threshold that was empirically determined (by us and in reference {{cite\|szlachta:prb:2014}}) is <math>\pm 0.02</math>. Hence, the number of basis functions should be adjusted until the error written in the {{TAG\|ML_LOGFILE}} is smaller than this value. A more detailed description of the basis sets is given in appendix A of reference {{cite\|jinnouchi2:arx:2019}}.



			== References ==
			<references/>

			<noinclude>
	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|ML_FF_LMLFF}}, {{TAG\|ML_FF_MRB1_MB}}, {{TAG\|ML_FF_W1_MB}}, {{TAG\|ML_FF_W1_MB}}, {{TAG\|ML_FF_RCUT1_MB}}, {{TAG\|ML_FF_RCUT2_MB}}, {{TAG\|ML_FF_SION1_MB}}, {{TAG\|ML_FF_SION2_MB}}		{{TAG\|ML_FF_LMLFF}}, {{TAG\|ML_FF_MRB1_MB}}, {{TAG\|ML_FF_W1_MB}}, {{TAG\|ML_FF_W1_MB}}, {{TAG\|ML_FF_RCUT1_MB}}, {{TAG\|ML_FF_RCUT2_MB}}, {{TAG\|ML_FF_SION1_MB}}, {{TAG\|ML_FF_SION2_MB}}

← Older revision		Revision as of 13:29, 8 April 2022
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	----		----

	[[Category:INCAR tag]][[Category:Machine ~~Learning]][[Category:Machine Learned Force Fields~~]]		[[Category:INCAR tag]][[Category:Machine-learned force fields]]